Force Test - 1

The centre of mass is that point where the entire mass of the two objects can be supposed to be concentrated. In case of two mass system, it lies closer to bigger mass.

When a body is moving with a constant velocity on a frictionless surface, acceleration is zero. Hence, no force is being applied on it.
This is because f = ma and if a is zero, then F is also zero.

When a constant acceleration is applied on the truck, the oil in the drums will rise in the backward direction because of inertia of rest. This principle states that a body has a tendency to not to leave its resting place. Hence, oil moves and rises backwards.

The weight of monkey acting downwards, W = mg = 20 × 10 = 200 N
The acceleration of monkey (a) = 7 m/s2
Force, F = ma = 140 N
ma = mg - T, where T is the tension in rope.
T = mg - ma
T = (200 - 140) N
T = 60 N

A parachutist of weight W strikes the ground with his legs fixed and comes to rest with an upward acceleration of 3g.
Let F is the upward force
ma = F - mg
m(3g) = F - mg
F = 3mg + mg = 4 mg
F = 4W

When a leather ball strikes a wall, all its energy is lost in sound and heat energy and it loses its momentum and falls down. But when a tennis ball hits a wall, it bounces back and hence it has momentum after hitting the wall. Therefore, a tennis ball suffers a greater change in momentum.

When it explodes into 2 fragments of equal masses, the momentum has to be conserved. The initial momentum is zero. Hence, final momentum should also be zero. This can be explained as below:
Here, V¹ and V² are velocities of two fragments and M is the initial mass.
M (0) = mv¹ + mv²
(From the law of conservation of momentum)
V¹ = – V²

Mass of body = M
Initial velocity = V
Initial momentum = MV
Final velocity = - V
Final momentum = - MV
Change = Final momentum - Initial momentum
Change = - MV - (MV)
= - 2MV